find all exact solutions in degrees?:?

Question

2sin^2(x) + cos(x) - 1 = 0

thanks!

cool yeah, I got the same thing but I didn't use the quad. formula.

Can anyone else verify?

you're answer's a little wrong and I think you forgot 240° tho

Answer 1

as sin^2(x) = 1-cos^2(x)
=> 2(1-cos^2(x)+cos(x)-1=0
=>2cos^2(x)-cos(x)-1=0
as we known the solution for ax^2_bx+c=0 are

(-b+- sqrt(b^2 - 4ac))/2a here +- means + and -

so cosx = (1+-sqrt(1+8))/(2*2) = (1+-3)/4 = -1/2, 1

equating this x = (2*PI)/(3*n) and n*PI

here PI is phi and n=0,1,2,...